Offline Reinforcement Learning with Differentiable Function Approximation is Provably Efficient

TL;DR

This paper provides a theoretical analysis demonstrating that offline reinforcement learning with differentiable function approximation is provably efficient, offering insights into the statistical complexity and practical heuristics.

Contribution

It introduces a formal analysis of offline RL with differentiable function classes, establishing provable efficiency and tighter guarantees for the PFQL algorithm.

Findings

Offline RL with differentiable function approximation is shown to be statistically efficient.

Theoretical analysis supports practical heuristics based on Fitted Q-Iteration.

Tighter, instance-dependent performance guarantees are provided.

Abstract

Offline reinforcement learning, which aims at optimizing sequential decision-making strategies with historical data, has been extensively applied in real-life applications. State-Of-The-Art algorithms usually leverage powerful function approximators (e.g. neural networks) to alleviate the sample complexity hurdle for better empirical performances. Despite the successes, a more systematic understanding of the statistical complexity for function approximation remains lacking. Towards bridging the gap, we take a step by considering offline reinforcement learning with differentiable function class approximation (DFA). This function class naturally incorporates a wide range of models with nonlinear/nonconvex structures. Most importantly, we show offline RL with differentiable function approximation is provably efficient by analyzing the pessimistic fitted Q-learning (PFQL) algorithm, and our results provide the theoretical basis for understanding a variety of practical heuristics that rely on Fitted Q-Iteration style design. In addition, we further improve our guarantee with a tighter instance-dependent characterization. We hope our work could draw interest in studying reinforcement learning with differentiable function approximation beyond the scope of current research.